Asymptotically Optimal Sequential Design for Rank Aggregation

A sequential design problem for rank aggregation is commonly encountered in psychology, politics, marketing, sports, etc. In this problem, a decision maker is responsible for ranking K items by sequentially collecting noisy pairwise comparisons from judges. The decision maker needs to choose a pair of items for comparison in each step, decide when to stop data collection, and make a final decision after stopping based on a sequential flow of information. Because of the complex ranking structure, existing sequential analysis methods are not suitable. In this paper, we formulate the problem under a Bayesian decision framework and propose sequential procedures that are asymptotically optimal. These procedures achieve asymptotic optimality by seeking a balance between exploration (i.e., finding the most indistinguishable pair of items) and exploitation (i.e., comparing the most indistinguishable pair based on the current information). New analytical tools are developed for proving the asymptotic results, combining advanced change of measure techniques for handling the level crossing of likelihood ratios and classic large deviation results for martingales, which are of separate theoretical interest in solving complex sequential design problems. A mirror-descent algorithm is developed for the computation of the proposed sequential procedures.

Hybrid Threshold-Based Sequential Procedures for Detecting Compromised Items in a Computerized Adaptive Testing Licensure Exam

Using classical test theory and item response theory, this study applied sequential procedures to a real operational item pool in a variable-length computerized adaptive testing (CAT) to detect items whose security may be compromised. Moreover, this study proposed a hybrid threshold approach to improve the detection power of the sequential procedure while controlling the Type I error rate. The hybrid threshold approach uses a local threshold for each item in an early stage of the CAT administration, and then it uses the global threshold in the decision-making stage. Applying various simulation factors, a series of simulation studies examined which factors contribute significantly to the power rate and lag time of the procedure. In addition to the simulation study, a case study investigated whether the procedures are applicable to the real item pool administered in CAT and can identify potentially compromised items in the pool. This research found that the increment of probability of a correct answer ( p-increment) was the simulation factor most important to the sequential procedures’ ability to detect compromised items. This study also found that the local threshold approach improved power rates and shortened lag times when the p-increment was small. The findings of this study could help practitioners implement the sequential procedures using the hybrid threshold approach in real-time CAT administration.

Pyrimidine-Based Push–Pull Systems with a New Anchoring Amide Group for Dye-Sensitized Solar Cells

New donor–π–acceptor pyrimidine-based dyes comprising an amide moiety as an anchoring group have been designed. The dyes were synthesized by sequential procedures based on the microwave-assisted Suzuki cross-coupling and bromination reactions. The influence of the dye structure and length of π-linker on the photophysical and electrochemical properties and on the photovoltaic effectiveness of dye-sensitized solar cells was investigated. An increase in efficiency with a decrease in the length of π-linker was revealed. The D1 dye with only one 2,5-thienylene-linker provided the highest power conversion efficiency among the fabricated dye sensitized solar cells.

Knockout-Tournament Procedures for Large-Scale Ranking and Selection in Parallel Computing Environments

On one hand, large-scale ranking and selection (R&S) problems require a large amount of computation. On the other hand, parallel computing environments that provide a large capacity for computation are becoming prevalent today, and they are accessible by ordinary users. Therefore, solving large-scale R&S problems in parallel computing environments has emerged as an important research topic in recent years. However, directly implementing traditional stagewise procedures and fully sequential procedures in parallel computing environments may encounter problems because either the procedures require too many simulation observations or the procedures’ selection structures induce too many comparisons and too frequent communications among the processors. In this paper, inspired by the knockout-tournament arrangement of tennis Grand Slam tournaments, we develop new R&S procedures to solve large-scale problems in parallel computing environments. We show that no matter whether the variances of the alternatives are known or not, our procedures can theoretically achieve the lowest growth rate on the expected total sample size with respect to the number of alternatives and thus, are optimal in rate. Moreover, common random numbers can be easily adopted in our procedures to further reduce the total sample size. Meanwhile, the comparison time in our procedures is negligible compared with the simulation time, and our procedures barely request for communications among the processors.

Speeding Up Paulson’s Procedure for Large-Scale Problems Using Parallel Computing

With the rapid development of computing technology, using parallel computing to solve large-scale ranking-and-selection (R&S) problems has emerged as an important research topic. However, direct implementation of traditionally fully sequential procedures in parallel computing environments may encounter various problems. First, the scheme of all-pairwise comparisons, which is commonly used in fully sequential procedures, requires a large amount of computation and significantly slows down the selection process. Second, traditional fully sequential procedures require frequent communication and coordination among processors, which are also not efficient in parallel computing environments. In this paper, we propose three modifications on one classical fully sequential procedure, Paulson’s procedure, to speed up its selection process in parallel computing environments. First, we show that if no common random numbers are used, then we can significantly reduce the computation spent on all-pairwise comparisons at each round. Second, by batching different alternatives, we show that we can reduce the communication cost among the processors, leading the procedure to achieve better performance. Third, to boost the procedure’s final-stage selection, when the number of surviving alternatives is less than the number of processors, we suggest to sample all surviving alternatives to the maximal number of observations that they should take. We show that, after these modifications, the procedure remains statistically valid and is more efficient compared with existing parallel procedures in the literature. Summary of Contribution: Ranking and selection (R&S) is a branch of simulation optimization, which is an important area of operations research. In recent years, using parallel computing to solve large-scale R&S problems has emerged as an important research topic, and this research topic is naturally situated in the intersection of computing and operations research. In this paper, we consider how to improve a fully sequential R&S procedure, namely, Paulson’s procedure, to reduce the high computational complexity of all-pairwise comparisons and the burden of frequent communications and coordination, so that the procedure is more suitable and more efficient in solving large-scale R&S problems using parallel computing environments that are becoming ubiquitous and accessible for ordinary users. The procedure designed in this paper appears more efficient than the ones available in the literature and is capable of solving R&S problems with over a million alternatives in a parallel computing environment with 96 processors. The paper also extended the theory of R&S by showing that the all-pairwise comparisons may be decomposed so that the computational complexity may be reduced significantly, which drastically improves the efficiency of all-pairwise comparisons as observed in numerical experiments.

Practical Synthesis of 2-Iodosobenzoic Acid (IBA) without Contamination by Hazardous 2-Iodoxybenzoic Acid (IBX) under Mild Conditions

We report a convenient and practical method for the preparation of nonexplosive cyclic hypervalent iodine(III) oxidants as efficient organocatalysts and reagents for various reactions using Oxone® in aqueous solution under mild conditions at room temperature. The thus obtained 2-iodosobenzoic acids (IBAs) could be used as precursors of other cyclic organoiodine(III) derivatives by the solvolytic derivatization of the hydroxy group under mild conditions of 80 °C or lower temperature. These sequential procedures are highly reliable to selectively afford cyclic hypervalent iodine compounds in excellent yields without contamination by hazardous pentavalent iodine(III) compound.